Name: log-rank test for comparing survival curves
Uploaded: 2025-01-09T15:14:16.000Z
Duration: 1 min 19 s
Channel: JoVE

マンテル-コックスのログランク検定は、2つのグループ間の生存分布曲線を比較するためのノンパラメトリック統計手法です。
通常、臨床研究で使用され、治療効果を経時的に評価し、さらなる研究を導くために使用されます。
たとえば、研究者はこの検定を使用して、新しい治療を受けているグループと対照治療を受けている別のグループの生存曲線との間に統計的に有意な差を判断できます。
Mantel-Cox検定では、特定の生存時間分布を仮定せずに、グループ間で観測された事象と予想される事象の差を計算します。これは、すべての被験者が死亡や病気の再発など、関心のあるイベントを経験するわけではない打ち切りデータの分析に最適です。
その限界は、時間の経過とともに一定のハザード比を仮定し、時には真実である可能性がある比例ハザードの仮定に対する信頼性にあります。このテストの結果は、比例ハザードの仮定に違反した場合、誤解を招く可能性があります。
これは、サンプルサイズが小さい研究や打ち切り率が高い研究に特に当てはまります。

mantel-cox ログランク検定

The Mantel-Cox Log-Rank Test

Mantel-Cox ログランク検定は、2 つのグループの生存分布を比較するために広く使用されている統計手法です。この検定は、生存データに特定の分布を想定せずに、グループ間の生存時間に統計的に有意な差があるかどうかを検定するため、ノンパラメトリック検定となります。この柔軟性により、ログランク検定は、死亡や病気の再発などのイベントのタイミングが重要な医学研究やその他の分野で特に役立ちます。臨床試験や疫学研究では、新しい治療法が対照治療や標準治療と比較して生存率を向上させるかどうかを評価するためによく使用されます。

ログランク検定の強みの 1 つは、打ち切りデータを処理できることです。打ち切りデータは、研究終了までに一部の対象で関心のあるイベントが観察されていない場合に発生します。この機能により、全ての参加者の完全な生存時間が利用できない場合でも、利用可能な全ての情報を検定に組み込むことができます。更に、この検定は生存時間が正規分布するという仮定に依存しないため、幅広い生存データに適しています。

ただし、ログランク検定には限界があります。グループ間のハザード比は時間の経過とともに比例して一定であると仮定していますが、この条件は常に当てはまるとは限りません。この仮定に違反すると、誤解を招く結果につながる可能性があります。更に、この検定では信頼性の高い結果を得るために十分な数のイベントが必要なため、サンプルサイズが小さい研究や打ち切り率が高い研究では効果が低くなります。このような場合は、Cox 比例ハザード モデルなどの代替手法の方が適している可能性があります。

Mantel-Cox ログランク検定は、その単純さにもかかわらず、様々な治療法が生存に与える影響を評価する強力で簡単な方法を提供します。イベントのタイミングと頻度の両方を考慮しているため、研究者は介入の有効性について有意義な結論を導き出すことができます。一定の限界はあるものの、適応性が高く、打ち切りデータで作業できるため、生存分析の重要なツールとなっています。

Mantel-Cox ログランク検定

マンテル-コックスのログランク検定は、2つのグループ間の生存分布曲線を比較するためのノンパラメトリック統計手法です。
それは通常採用されています...

Education

JoVE Core

Statistics

統計

Unit 1

ユニット1

Survival Analysis

生存解析

KEY TERMS AND CONCEPTS

主要用語と概念

log-rank test for comparing survival curves

The Mantel-Cox log-rank test compares survival curves from two groups. It checks whether the groups have a statistically significant difference in survival time. This makes it useful when the timing of an event matters, such as death or disease recurrence.

The log-rank test is non-parametric. That means it does not assume a specific distribution for the survival data. It is also useful in medical research, where it often helps compare a new treatment with a control or standard treatment in clinical trials and epidemiological studies.

A key strength of the test is that it can handle censored data. Censored data means the event has not been observed for some subjects by the end of the study. The test can still use that information, even when complete survival times are not available for every participant.

The test also does not rely on normally distributed survival times. That makes it suitable for many kinds of survival data. However, it assumes that the hazard ratios between groups stay proportional and constant over time, and that may not always be true.

If this assumption is violated, the results can be misleading. The test also needs enough events to give reliable findings. It is less effective when sample sizes are small or censoring is high, so a Cox proportional hazards model may be a better choice in those cases. Even with these limits, the Mantel-Cox log-rank test remains a simple and powerful tool for judging how treatments affect survival.

Log-Rank Test for Comparing Survival Curves

log-rank-test-for-comparing-survival-curves

introduction to survival analysis

Time-to-Event Data and Censoring

Survival analysis is a statistical method for time-to-event data. The event can be death, disease relapse, system failure, or recovery. It helps estimate survival time, which is the time until a specific event occurs, and it also shows what factors may affect that time. A key idea in survival analysis is censoring. Censoring happens when the event of interest has not been observed for some people during the study period. Because the data are incomplete in those cases, survival analysis uses...

life tables

Life Tables and Survival Patterns

A life table is a statistical tool that shows mortality and survival patterns in a population. It organizes data across age intervals so students can see how likely a group is to survive or die at each stage of life. The table gives a clear snapshot of population dynamics over time. Life tables are used in demography, public health, actuarial science, and ecology. They help scientists study life expectancy, plan health interventions, estimate insurance risk, and compare how species survive in...

survival curves

Kaplan-Meier Survival Curve Basics

Kaplan-Meier survival curves show how the chance of staying event-free changes over time. They are used to track survival in a population and to compare groups in medicine, public health, and reliability engineering. The Kaplan-Meier estimator is the most common way to build these curves. It is a non-parametric method, which means it does not assume a fixed pattern for the data. The result is a stepwise line that drops each time an event happens, such as death, disease recurrence, or...

actuarial approach

Life Table Method for Survival Rates

The life table method, also called the actuarial approach, is used to estimate survival rates in clinical and population studies. It began in life insurance, where risk over time must be measured carefully. In health research, it gives a clearer picture of survival when some participants are lost to follow-up or die from causes unrelated to the study. This method works by dividing the study period into set intervals, usually one year. That makes it useful for tracking outcomes over time,...

kaplan-meier approach

Survival Curves with Kaplan-Meier Data

The Kaplan-Meier estimator is a non-parametric method for estimating a survival function from time-to-event data. It is commonly used in medical research to track how many patients survive for a set time after treatment. It is also important in clinical trials, epidemiological studies, and reliability engineering. This method helps researchers study survival probabilities over time, even when some data are incomplete. That incomplete data is called censored data, which means the exact event...

assumptions of survival analysis

Survival Analysis Assumptions in Studies

Survival analysis studies the time until an event happens. The event may be death in a living organism or failure in a mechanical system. These models are used in medicine, biology, engineering, and public health to study time-to-event data. Careful study design matters because the method depends on several key assumptions. One common feature of survival times is positive skewness. This means events often happen early, while fewer cases occur later. Survival data also often include censoring,...

comparing the survival analysis of two or more groups

comparing-the-survival-analysis-of-two-or-more-groups

Kaplan-Meier Curves and Hazard Ratios

Kaplan-Meier curves and hazard ratios help researchers compare survival time between groups. Survival analysis looks at the time until an event happens, such as death, disease recurrence, or recovery. It is a key tool in medical research. A major strength of survival analysis is that it can handle censored data. Censored data means the event has not happened for some participants by the end of the study, or it has not been observed. This makes survival analysis different from standard...

the mantel-cox log-rank test

The Mantel-Cox log-rank test compares survival curves from two groups. It checks whether the groups have a statistically significant difference in survival time. This makes it useful when the timing of an event matters, such as death or disease recurrence. The log-rank test is non-parametric. That means it does not assume a specific distribution for the survival data. It is also useful in medical research, where it often helps compare a new treatment with a control or standard treatment in...

applications of life tables

Life Tables in Public Policy and Science

Life tables are used in many fields to study mortality and survival rates. They give a numerical way to examine how long people or living things are likely to survive. This makes them useful for public health, business planning, and scientific research. In demography and public health, life tables help experts study population changes and predict future trends. They can show patterns such as an aging population or the effect of a health policy. In Nigeria, health officials used survival rates...

cancer survival analysis

Cancer Survival Curves and Risk Factors

Cancer survival analysis measures how long it takes from diagnosis or the start of treatment to a specific outcome, such as remission or death. It helps researchers judge treatment effectiveness and understand what affects patient outcomes. These results also support clinical decisions and prognostic evaluations. Survival data are often skewed and not normally distributed. They also include censored cases, where the full survival time is unknown because the study ends, a patient is lost to...

hazard rate

Modeling Event Risk Over Time

Hazard rate is a statistical measure that describes how event risk changes over time. It is also called the hazard function or failure rate. In survival analysis, it shows the instantaneous rate at which an event occurs, but only after the subject has not had the event yet. From a probability view, hazard rate gives the chance that a subject will have the event in a very small time interval. That chance is conditional on surviving to the start of that interval. From a frequency view, it can...

hazard ratio

Hazard Ratio in Clinical Trials

The hazard ratio is a way to compare event risk in clinical trials. It is often used to study events such as death or disease recurrence in two groups over time. The two groups are usually a treatment group and a control group. A hazard ratio compares hazard rates, which are the instantaneous risk of an event happening at a given moment. It shows how the risk in one group relates to the risk in the other group. In a cancer drug study, for example, the hazard ratio can show how a new treatment...

truncation in survival analysis

Left and Right Truncation in Survival Data

Truncation in survival analysis describes data loss caused by the timing of an event or by when a subject can enter a study. It can happen in two forms: left truncation and right truncation. In both cases, some individuals are left out of the dataset before analysis begins. Left truncation happens when people who had the event before a set time are not included in the study. This often occurs with delayed entry, which means a person is only observed if they survive until the entry point. For...

censoring survival data

Types of Censoring in Survival Analysis

Survival analysis studies time-to-event data, which tracks how long it takes for an outcome to happen. It is used in medicine, engineering, and social science. A common problem in this type of data is censoring, which means the full event time is not observed for every person or item. Censoring can happen for several reasons and in different patterns. The most common kind is right censoring. This happens when the event has not occurred by the end of the study or when a participant is lost to...

survival tree

Survival Tree in Time-to-Event Analysis

A survival tree is a non-parametric tool in survival analysis that links predictor variables, or covariates, to survival time. Survival time is the time until an event of interest occurs. It is useful when some data are censored, which means the event has not happened for some people by the end of the study or the exact event time is unknown. Building a survival tree starts with a dataset that includes covariates, survival time, and a censoring indicator for each subject. The data must be...

parametric survival analysis: weibull and exponential methods

parametric-survival-analysis-weibull-and-exponential-methods

Modeling Survival Time with Weibull and Exponential

Parametric survival analysis models survival time by assuming a specific probability distribution for when an event occurs. The Weibull and exponential distributions are two common choices because they are flexible and relatively straightforward to use. The Weibull distribution is a flexible model in parametric survival analysis. It can describe both increasing and decreasing hazard rates, depending on its shape parameter beta. When beta is greater than 1, the hazard rate rises over time. That...

key terms and concepts

Learn how the Mantel-Cox log-rank test compares survival curves, handles censored data, and helps assess treatment effects in survival analysis.

Log-Rank Test for Comparing Survival Curves | JoVE K12

statistics

JoVE Core 統計は、データの収集、分析、表示、解釈の概念と応用を学生に紹介します。これらのアニメーション授業は、幅広い分野の学生にとって有益な統計の理解を提供します。さらに、科学者が実際に活動しているビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

Log-Rank Test for Comparing Survival Curves

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